Clutch or brake

ABSTRACT

A friction brake or friction clutch in which the wear-resistant brake or clutch surface or surfaces and the associated brake or clutch lining or linings which are adapted to be worn consist of equal sets of directly adjacent teeth of an isosceles triangular shape which fully interengage with each other when the brake or clutch is engaged.

I United States Patent 1 91 11 1 3,750,788 Heinemann 5 Aug. 7, 1973 CLUTCH R BRAKE 2,983,351 1961 Hindmarch 192 107 M 2,965,205 12 1960 W h ll 1-92 107 R [76] Invent: Rm 'f f 3,386,122 61968 14:1 :15; 192107 R 1 28, 7000 Stuttgart 7O (Pllenmgen), G r FOREIGN PATENTS OR APPLICATIONS 1 440,674 6/1925 Germany 192/107 R [22] 1971 743,192 1 1/1956 Great Britain 192 107 M [21] Appl. No.: 196,546

Primary Examiner-Charles .l. Myhre Assistant Examiner-Randall Heald Foreign Application Priority Data Atmmey Anhur O Klein Nov. 12, 1970 Germany P 20 678.0

52 U.S. c1 192/107 R, 188/713, 192/7014 [57] ABSTRACT 1511 1111. c1. F1611 11/00 A friction brake r friction clutch in which the Wear- 53] Fi ld f Search 192 107 M, 07 R, resistant brake or clutch surface or surfaces and the as- 192/70 14; 133 213 XL 713 sociated brake or clutch lining or linings which are adapted to be worn consist of equal sets of directly ad- 56 R f Ci jacent teeth of an isosceles triangular shape which fully UNITED STATES PATENTS interengage with each other when the brake or clutch 896,389 8/1908 Johnston 192 107 R engaged 951,992 3/1910 Johnson 192/107 R 12 Claims, 11 Drawing Figures PATENIEDAHQ um 3750(788 SHEET 1 9f 3 PAIENIED SHEET 2 [IF 3 1" cwrcnon BRAKE The present invention relates to a brake or friction clutch which comprises at least onepair of friction surfaces whichareadapted to be moved relative to each a row of ribs or teeth which have an equal crosssectional shapewith inclined flanks and extend in the direction in which the brake or, clutch is engaged and disengaged.

Generally speaking, the associated friction surfaces of brakes or friction clutches ofa disk-shaped or drumshaped construction have substantially plane or cylindrical cross-sectional shapes, Although it has also been proposed to provide the friction surfaces in the form of trapezoidal ribs of a relatively great height, the con-,

struction of such clutches or brakes has again been abandoned because it wasyfoun'dthatthe trapezoidal shape and great height of the ribs causes a series of disadvantages.

it is an object of thepresent invention to provide a brake or friction clutch which has the highest possible rate of economy 'andoperational efficiency, that is, a rate much higher than that of any of the friction clutches or brakes as were "known prior to this invention. n

For attaining this object, the invention provides a brake or friction clutch {of the type as described in the first paragraph above in which the friction surface of the brake 'orclutch memberwhich consists of a wearresis'tant materialis formedentirely by the-flanks of the ribs or teeth which are located immediately adjacentto each other and each of which has a cross-sectional shape of a triangleofa heightwhich amounts approximately toone-fifth to one-tenth of the maximum thickness of the partofthe associated clutch or brake member which consists of a material which is intended to be worn off gradually, during the subsequent use of the clutch oi'jbrake. ltisanother requisite feature of the in-, vention that at least when the brake or clutch is broken in the angle a at which each flank of the teeth of each clutch orbrakemember is disposed relative to a common plane from which all of the teeth project at a right angle has a size within arange in which the tangent of a is larger than the coefficient of friction p. of the two clutch or brake members on each other.

i When changing the usual plane orcylindrical friction surfaces of such a brake or clutch to such a, serrated cross-sectional shape it is possible when pressing these surfaces against each other with the same force as previously employed to increase the friction between them to at least twice the previous value. This increased friction which does not require the friction surfaces to be made of any materials different from those which are conventionally used for such clutches or brakes permits a clutching or braking operation to be carried out very effectively by means of a much smaller muscular force than was previously required or merely by a muscular force when previously a force amplifier had to be used. When using the same force as previously, it is now also possible to produce the same frictional force by making the friction surface of the brake or clutch, member which consists ofa wearable material, forexample, that of a brake or clutch lining, ofpa material which pro-.

duces a lower coefficient of friction and usually has a higher wear resistance, so that the brakeor clutch requires less service or may not require any service at alll Since the ribs or teethonly have to have a relatively low height, the costs of producing them are very low.

This is important especially if the materials of which they aremade can be machined only with difficulty. By making the teeth of a triangular cross section, those which consist of a wearable material also do not have to be provided with ribs or teeth, and because of the low height of the teeth, it will require only a short time until the wear-resistant teeth of one clutch or brake mamber have worn' exactly corresponding grooves into an originally plane or cylindrical surface of the other member of a wearable material or untl theyhaveworn 'all teeth of both members when applied upon each other will be in full engagement with each other. Since the teeth or ribsgrooves only have to be provided in the clutch or brake member which consists of a wear resistant'material, the difficulty andcosts of producing the other clutch or brake member of a wearable'mate rial will be reduced and the latter may even be made of a material which cannot be normally machined eco nornically; i

By making-the teeth ofa very small size, the wearable material, for example, that of a brake or clutch lining, may be worn to such an extent that when the latter permits nofurther wear by the wear-resistant teeth of the other clutch or brake member without causing perma? nent damage to the clutch or brake, only a set of teeth will practically remain of n the wearable material which has a very small volume ascornpared with the original volume of this member. Furthermore, duringthe entire wear upon {this member the friction between both members will not vary. Therefore, contrary to 21 clutch or brake with teeth of a trapezoidal, shape, the wear upon the wearable member is not limited tothe height of the original teeth thereon or to the height of the teeth as originally worn into thisrnernber by the wearresistant teethof the other member, but the wearable member may be worn offalrnost completely, Since there is no need to interrupt the friction surface of the wearable member, i.e., the surfaces of its teeth, by

teeth 'or'ribs which were previously also required, the

still ,on its side which is to be secured to this clutchor brake member with a set of teeth of a size and shape corresponding, to the tee'th on its other side or to. be worn into this other side by gthe wear resistant teeth of the other member. The-two sets of teeth on this lining should, however, be offsetilaterally relative to each other at a distance of one half tooth. in this event, the

wear-resistant teeth may wear off the material of the lining almost entirely and almost to the roots of the teeth which are provided in the other clutch or brake member for carrying the lining.

It is a further advantage which is attained by making the friction surfaces of a clutch or brake of the serrated shapeas. described that the clutch or brake lining may be made relatively thin.

The triangular cross section of the teeth permits them to form a continuous uninterrupted row so that the entire surface area which is formed by the flanks of these teeth may be utilized for producing the desired friction, that is, a friction which is considerably increased over that which is attainable if the friction surfaces are plane or cylindrical. If therefore a predetermined normal force is applied for pressing the two clutch or brake members against each other, the friction surface of the wearable part or lining on one clutch or brake member will be subjected by the other member only to a minimum of pressure per square inch. Furthermore, if the angle a of the flanks of the teeth of both clutch or brake members is made of a size within a range in which the tangent of a has a larger value than the coefficient of friction, there will be no danger that, when the two clutch or brake members are to be disengaged from each other, any binding or locking effect might occur between the teeth of both clutch or brake members.

The highest possible frictional force may be attained if the angle a of the tooth flanks is made of such a size that the ratio between the coefficient of friction and the sine of the angle a will have approximately a value of 1. However, in some cases in which, for example, in an order of clutches or brakes of the same outer dimensions some of these clutches or brakes should produce a different frictional force than the others, it may be desirable to make the angle a ofa size which will not produce the highest possible friction. This may also be done, for example, by making the angles of the two flanks of each tooth of different sizes.

Another feature of the invention consists in providing the two associated clutch or brake members with abutments which will engage with each other when the part of the wearable material of one member, for example, the lining of such a material, has been worn off to the greatest permissible extent by the wear-resistant teeth of the other member so that these teeth cannot possibly grind into, or be ground off or damaged otherwise by, the clutch or brake member itself which carries this part or lining.

The brake or clutch according to the invention may be either of a disk-shaped or drum-shaped construction since the two sets of friction teeth may be either provided on associated brake or clutch members which are movable relative to each other in the direction of the axis of rotation of at least one of these members, and these two sets then project toward each other from the sides of these members which extend vertically to this axis of rotation, or these two sets of teeth may be provided on a peripheral surface of a drum-shaped clutch or brake member and on at least one clutch or brake member which may be pressed against this peripheral surface.

The features and advantages of the present invention will become more clearly apparent from the following detailed description thereof which is to be read with reference to the accompanying drawings, in which FIG. 1 shows diagrammatically a longitudinal section of a part of a disk clutch or disk brake;

FIG. 2 shows a front view of the friction surface of the friction disk according to FIG. 1 which consists of a highly wear-resistant material;

FIG. 3 shows an enlarged view of a part of FIG. 1;

FIG. 4 shows a view which is similar to FIG. 4, but in which the two friction surfaces are separated at a sufficient distance from each other as may be required for disengaging the clutch or brake;

FIG. 5 shows an enlarged sectional view of a clutch or brake similar to that as shown in FIGS. 3 and 4 but in which before the clutch or brake is used for the first time, that is, before it has been broken in, only the highly wear-resistant friction surface has a serrated cross section;

FIG. 6 shows a view of the part of the clutch or brake according to FIG. 5 in a condition while being broken FIG. 7 shows diagrammatically a longitudinal section of a part of a clutch or brake which is operated electromagnetically;

FIG. 8 shows dlagrammatically a longitudinal section of a part of another embodiment of the invention in the form of a brake;

FIG. 9 shows diagrammatically a longitudinal section of a part of another embodiment of the invention in the form of a combination of a clutch and a brake;

FIG. 10 shows diagrammatically a cross section of another embodiment of the invention in the form of a drum brake; while 7 FIG. 11 shows an enlarged view of a art of the brake according to FIG. 10.

In the drawings, FIGS. 1 and 2 show a part of a friction disk clutch or friction disk brake all parts of which other than those specifically described herein may be of a conventional construction and which comprises a cylindrical friction disk I of metal which in this particular embodiment of the invention is integral with its hub 2. This friction disk 1 and its hub 2 extend coaxially to a disk 4 and its hub 3 which are rotatable together relative to the friction disk 1 about a common axis. In addi tion, disk 4 may be shifted in its axial direction relative to friction disk I by suitable means, not shown, for pressing it against the annular surface forming the friction surface 6 of disk 1. The side of disk 4 facing the annular surface of disk 1 carries an annular friction member or lining 5 which forms the second friction member and consists of a friction material of which such linings or the like are usually made. This friction lining 5 has inner and outer diameters substantially corresponding to those of the friction surface 6 of disk 1.

The friction clutch or friction brake according to the invention differs essentially from those of a conventional construction by the fact that the entire friction surface 6 of the disk 1 is provided in the fonn of annular. ribs or teeth 7 which extend concentrically to the axis of rotation, all have an equal size and an equal cross-sectional shape of an isosceles triangle, and are directly adjacent to each other. In this particular embodiment of the invention as shown more clearly in FIGS. 3 and 4, each of these teeth 7 projects from the disk 1 at an angle of and each flank of each tooth extends at an angle a of 30 to the center of the tooth. The height of these teeth 7 may amount to about 0.5 mm up to about 1 mm.

The friction surface of the friction member or lining 5 facing the friction surface 6 of disk 1 is likewise provided in the form of annular ribs or teeth 8 which have a cross-sectional shape corresponding to that of the teeth 7 and are radially offset by one half tooth relative to the latter so that, when disk 4 is shifted toward the friction element to the position as shown in FIG. 3, the corresponding flanks of all teeth 7 and 8 will engage upon each other. Teeth8 therefore also have the same height as the teeth 7.

The increase of the frictional force which may be attained whenthe flanks of teeth 7 and Bare pressed against each other as compared with the frictional forcewhich is attainable between two plane or cylindrical friction surfaces equals the reciprocal value of the sine of the flankangle a. If the normal force with which the friction lining 5 is pressed against the friction surface 7 is calIed P the coefficient of friction of the two materials of which the friction surfaces of teeth 7 and 8 is called p. and the frictional force attainable is called P this last force will amount to a P (I/sine a) p. P

The factor (l/sine a) maybe called the increasing factor by which the frictional force is increased due to the cross-sectional shape of the toothlike friction surfaces over the frictional force which is attainable between two plane friction surfaces when the pressure P is equal in both cases. This increasing factor solely de- Coefficient Flank of Friction Angle tg sine Increasing p. a a a Factor llsine a 0.5 30 0.59 1 0,500

The teeth may be made of a. relatively low height.

Good results may still be attained if at a total thickness of the friction lining 5 of, for exa inple, 5 mm, the height of the teeth amounts to one-tenth to one-fifth of this thickness.

The gap which is required for disengaging the flanks of teeth 7 and 8 and thus their friction surfaces from each other may be made very small, as indicated in FIG. 4. Disk 4 therefore only needs to be shifted for a very small distance relative to disk 1 to press it against or to retract it from the latter. 1

As illustrated in FIG. 2, the friction. surface 6 is provided with grooves 9 which extend in radial directions through the teeth 7 and have a depth greater than the height of these teeth. These grooves 9 serve for removing the dust which might be produced by the wear of teeth 7 on the surfaces of teeth 8. All of these grooves are equal and the radii in which they are provided also extend from the axis of disk 1 at equal angles relative toeach other. While in the case as shown in FIG. 2 disk 1 is provided with eight of these grooves 9, their number may also be larger or smaller. Disks 1 and 4 are further provided with annular shoulders 10 and II which are adapted to abut against each other when the teeth 7 on disk 1 have worn off the friction lining 5 to the greatest permissible extent.

The embodiment of the invention as illustrated in FIGS. 5 and 6 differs from that as shown in FIGS. 1 to 4 merely by the fact that originally only disk 1' which consists of a highly wear-resistant material is provided with teeth 7', while the annular friction lining 5' which nally has an unserrated surface. Before it can be used effectively, the clutch or brake must therefore first be broken in by pressing the two disks against each other until the teeth 7 have ground corresponding teeth into the lining 5. However, it will only take a relatively short time until the teeth 7 which have only a low height, as pointed out with reference to FIGS. 1 to 4, will-wear tooth gaps of such a depth into the surface of lining 5 that between these tooth gaps teeth 8 are formed, as shown in FIG. 6, which have approximately one half of the height of the teeth 7'. By numerous tests it has been found that, when the two friction disks are pressed in this condition against each other,the clutching or braking effect between the parts of the flanks of teeth 7' which engage with the flanks of the only partly fonnedteeth 8' will already be substantially the same as the clutching orbraking effect which will be attained if the teeth 7' are fully worn into the lining 5' and have formed corresponding teeth therein and the flanks of both sets of teeth are fully in engagement with each other. l l i FIG. 7 illustrates another embodiment of the inventionin the form of an electromagnetically actuated clutch or brake the friction surfaces of which have again a serrated cross section like those of the embodiment as shown in FIGS. 1 to 4. However, in this case the annular serrated friction lining I05 which is adapted to engage with the teeth on the metallic disk 104 on a hub 103 is secured to a brake or clutch member 101 which is mounted concentrically todisk 104 and has an annular part 1 1 1 of a U-shaped cross section the open side of which faces disk I04 and is closed by the friction lining 10S. Into the space within the U- shaped part 111 of the brake or clutch member 101 an annular magnet coil 1 12 is inserted. The friction lining 105 is mounted between the free ends of the two arms of the U-shaped part 111 through which the magnetic flux which is produced when coil 1 12 is energized flows into disk 104 and thereby draws the serrated friction surface of the latter against the corresponding serrated friction surface of the lining 105. FIG. 8 shows a further embodiment of the invention in the form of a brake in which a rotatable brake disk 204 is provided on both lateral sides of an annular end part with-wear-resistant serrations similar to those as described with reference to FIGS. .1 to 4. Against both of these sets of serrations at least two nonrotatable brake shoes 205 and 205 which are provided with corresponding serrations are adapted to be moved simultaneously in opposite directions parallel to the axis of rotationof disk 204. These brake shoes may consist either entirely of a material which is conventionally used for brake linings or at least the parts thereof facing disk 204 and terminating into the serrations which are adapted to engagewith the serrations on disk 204 may consist of a wearable material.

FIG. 9 illustrates the present invention as being applied to the combination of a clutch and a brake. A disk 316 is nonrotatably connected to a driven shaft 315 but slidable in opposite axial directions along or together with this shaft. On each lateral side, this disk 315 carries an annular friction lining 305 or 305', respectively, which extends coaxially to shaft 315 and is provided on its outer side with a set of teeth similar to the teeth 8 on the lining 5 as shown in FIGS. 1 to 4. By a movement of disk 316 toward the left of FIG. 9, the serrated side of the friction lining 305 may be pressed against a corresponding set of teeth on a clutch disk 317 which is nontatably connected to a drive shaft 318, while by a movement of disk 316 toward the right of FIG. 9 this disk will be disengaged from the clutch disk 317 and the serrated side of the other friction lining 305' may be pressed against a corresponding set of teeth on a relatively stationary brake member 319. By providing both sides of disk 316 with serrated friction linings 305 and 305, disk 316 may be connected either by muscular force or by suitable means with a high friction either with the serrated side of clutch disk 317 or with the serrated side of brake member 319.

In order to prevent the teeth on clutch disk 317 or on the brake member 319 from engaging with disk 316 when one or the other friction lining 305 or 305' has been worn off, clutch disk 317 as well as brake member 319 is provided with an annular shoulder 320 or 321, respectively, which will engage with disk 316 when the lining 305 or 305' has been worn off to the greatest admissible extent.

FIGS. 10 and 11 illustrate the application of the invention to a drum brake which is of a conventional construction with the exception of the serrated shape of its brake surfaces and of the back of the brake linings and the surfaces of the brake jaws carrying these linings. This brake comprises a drum 401 of metal the inner peripheral side of which forms a friction or brake inner peripheral side of which forms a friction or brake surface which consists of a set of wear-resistant teeth 408 extending parallel and directly adjacent to each other and coaxially to the axis of rotation of the drum. Each of these teeth 408 has again a cross-sectional shape of an isosceles triangle which in this particular case forms an angle of 60 so that the angle a between each flank of each tooth relative to a plane extending at right angles to the axis of rotation of the drum through the tip of the tooth amounts to 30.

At the inside of drum 401 two jaws 404 are mounted in a conventional manner and are adapted to be pressed against the action of springs, not shown, against the serrated brake surface 408 of the drum. Each of these jaws 404 carries a brake lining 405 the outer side of which is provided with a set of teeth 407 which exactly correspond to the teeth 408 on brake drum 401 and are adapted fully to engage with these teeth when the brake is applied and to be retracted therefrom by thesprings acting upon the jaws 404 when the brake is released. On its inner side, each brake lining is provided with another set of teeth 407' which are equal to the outer teeth 407 but are offset at a distance of one half tooth in the axial direction of the drum relative to the teeth 407. The innerperipheral surface of drum 401 is also provided with a set of teeth which exactly correspond to the lining teeth 407' and to the surface of which the latter may be secured. All teeth 407, 408, 407' and those on the brake jaws 404 are therefore identical in size, shape and pitch, but teeth 407 are offset in the axial direction of the drum by the distance of one half tooth relative to the teeth 407.

By providing these teeth 407' on the brake linings 405 and the corresponding teeth to which they are secured on the brake jaws 404 and by offsetting these teeth 407' by the distance of one half tooth relative to the teeth 407, the advantage is attained that the brake linings 405 can be worn off practically entirely by the teeth 408, whereas if the inner surfaces of the-brakelinings and the outer surfaces of the brake jaws 404 to which the brake linings are secured were cylindricalrather than serrated and the brake linings were worn off until the tips of the teeth 408 on drum 401 would touch the outer surfaces of brake jaws 404, a loose set of adjacent teeth of brake-lining material would remain and be wasted as a residue of each brake lining. Of course, such a double set of teeth may also be provided on the linings of clutches and brakes of a disklike-construction.

Although my invention has been illustrated and described with reference to the preferred embodiments thereof, I wish to have it understood that it is in no way limited to the details of such embodiments but is capable of numerous modifications within the scope of the appended claims.

Having thus fully disclosed my invention, what 1 claim is:

l. A friction brake or friction clutch comprising at least one first and one second member at least oneof which is movable back and forth to the other for disengaging and engaging said members and both members having parts with friction surfaces facing each other, said part of the first of said members consisting of a wear-resistant material and said part of the second member consisting of a wearable material adapted to be worn when at least one of said members is pressed against the other, said friction surface of both of said parts being serrated at least when said brake or clutch is fully broken in and then consisting of teeth extending concentric with the axis of rotation of the respective part and parallel to the direction of the relative slidingmovement between said members and all of-said teeth having the same cross-sectional size and shape and having inclined flanks forming the entire friction surface of each part so that the flanks of said teeth of each part are located directly adjacent to each other so as to form a continuous row, each of said teeth including the common base of all teeth of the same part then having a triangular cross section of a height of at least approximately one-fifth to one-tenth of the thickness of said wearable part before being worn, the angle a of each flank of said teeth relative to a plane extending vert'ically to said common base which extends in the longitudinal direction of said teeth having a tangent larger than the coefficient of friction a between the teeth of both parts when pressed against each other.

2. A brake or clutch as defined in claim 1, in which each of said teeth of both parts together with its base has an isosceles triangular cross section at least when said brake or clutch is fully broken in. g

3. A brake or clutch as defined in claim 1, in which the angle a of each flank has such a size that the ratio betweeen the coefficient of friction p. and the sine of the angle a has approximately a value of l.

4. A brake or clutch as defined in claim 1, in which the angle a has a size of 15 to 30". i

5. A brake or clutch as defined in claim 1, in which the friction surfaces of both of said members which are adapted to engage with each other have a corresponding cross-sectional shape at least when said brake or clutch is fully broken in. j

6. A brake or clutch as defined in claim 1, in which said wearable part forms a friction lining which is connected to a supporting surface of said second member,

said supporting surface also having a serrated crosssectional shape corresponding to that of the wearresistant surface of said first member, and the surface of said lining which is connected to said supporting surface having a serrated cross-sectional shape corresponding to that of said supporting surface.

7. A brake or clutch as defined in claim 1, in which said two members are provided with shoulders facing each other and adapted to engage with each other for preventing said wear-resistant teeth of said first member from wearing off said wearable part excessively.

8. A brake or clutch as defined in claim 1, in which at least one of said members is rotatable about a central axis and at least one of said members is movable back and forth relative to the other member in the direction of said axis, the corresponding flanks of said teeth of said wearable and wear-resistant parts having equal angles a at least when said brake or clutch is fully broken 9. A brake or clutch as defined in claim 8, in which at least said first member having said wear-resistant part is rotatable, said first member having grooves extending transverse to the longitudinal direction of said teeth and being substantially equally spaced'from each other and having a depth greater than the height of said teeth of said wear-resistant part.

10. A brake orclutch as defined in claim 1, in which one of said members is drum-shaped and the serrated friction surface of said member is disposed within a peripheral surface of said member.

11. A brake or clutch as defined in claim 1, in which. only said friction surface of said wear-resistant part of said first member was initially serrated, the friction surface of the wear-resistant part of said first member having thereafter worn its teeth into the originally unscrrated wearable part of said second member.

12. A brake or clutch as defined in claim 1, wherein the wear-resistant part of the first member is made of metal, and the wearable part of the second member is made of friction brake-lining material. 

1. A friction brake or friction clutch comprising at least one first and one second member at least one of which is movable back and forth to the other for disengaging and engaging said members and both members having parts with friction surfaces facing each other, said part of the first of said members consisting of a wear-resistant material and said part of the second member consisting of a wearable material adapted to be worn when at least one of said members is pressed against the other, said friction surface of both of said parts being serrated at least when said brake or clutch is fully broken in and then consisting of teeth extending concentric with the axis of rotation of the respective part and parallel to the direction of the relative sliding-movement between said members and all of said teeth having the same cross-sectional size and shape and having inclined flanks forming the entire friction surface of each part so that the flanks of said teeth of each part are located directly adjacent to each other so as to form a continuous row, each of said teeth including the common base of all teeth of the same part then having a triangular cross section of a height of at least approximately one-fifth to one-tenth of the thickness of said wearable part before being worn, the angle Alpha of each flank of said teeth relative to a plane extending vertically to said common base which extEnds in the longitudinal direction of said teeth having a tangent larger than the coefficient of friction Mu between the teeth of both parts when pressed against each other.
 2. A brake or clutch as defined in claim 1, in which each of said teeth of both parts together with its base has an isosceles triangular cross section at least when said brake or clutch is fully broken in.
 3. A brake or clutch as defined in claim 1, in which the angle Alpha of each flank has such a size that the ratio between the coefficient of friction Mu and the sine of the angle Alpha has approximately a value of
 1. 4. A brake or clutch as defined in claim 1, in which the angle Alpha has a size of 15* to 30*.
 5. A brake or clutch as defined in claim 1, in which the friction surfaces of both of said members which are adapted to engage with each other have a corresponding cross-sectional shape at least when said brake or clutch is fully broken in.
 6. A brake or clutch as defined in claim 1, in which said wearable part forms a friction lining which is connected to a supporting surface of said second member, said supporting surface also having a serrated cross-sectional shape corresponding to that of the wear resistant surface of said first member, and the surface of said lining which is connected to said supporting surface having a serrated cross-sectional shape corresponding to that of said supporting surface.
 7. A brake or clutch as defined in claim 1, in which said two members are provided with shoulders facing each other and adapted to engage with each other for preventing said wear-resistant teeth of said first member from wearing off said wearable part excessively.
 8. A brake or clutch as defined in claim 1, in which at least one of said members is rotatable about a central axis and at least one of said members is movable back and forth relative to the other member in the direction of said axis, the corresponding flanks of said teeth of said wearable and wear-resistant parts having equal angles Alpha at least when said brake or clutch is fully broken in.
 9. A brake or clutch as defined in claim 8, in which at least said first member having said wear-resistant part is rotatable, said first member having grooves extending transverse to the longitudinal direction of said teeth and being substantially equally spaced from each other and having a depth greater than the height of said teeth of said wear-resistant part.
 10. A brake or clutch as defined in claim 1, in which one of said members is drum-shaped and the serrated friction surface of said member is disposed within a peripheral surface of said member.
 11. A brake or clutch as defined in claim 1, in which only said friction surface of said wear-resistant part of said first member was initially serrated, the friction surface of the wear-resistant part of said first member having thereafter worn its teeth into the originally unserrated wearable part of said second member.
 12. A brake or clutch as defined in claim 1, wherein the wear-resistant part of the first member is made of metal, and the wearable part of the second member is made of friction brake-lining material. 